Authorities said Atkins fired at officers during the pursuit and that they returned gunfire after he crashed and ran into the Trader Joe's.

The man is believed to have gone on the run after shooting his grandmother and girlfriend. Their conditions were not given.

The woman has not officially been identified, but ABC News named her as Melyda Corado, the store manager, citing family sources.

Frightened customers and workers dived for cover as police bullets fired at the man shattered the store's glass doors.

About three hours later, Atkins - who had been shot in the left arm - agreed to handcuff himself and walked out the front door, surrounded by four of the hostages.

At a news conference afterward, Los Angeles Mayor Eric Garcetti said a woman inside Trader Joe's had been killed.

His grandmother had tried to help him find employment and "was just trying to make him do better", she said. It is unclear if the fatal shot was sacked by the gunman or a police officer, he said. The suspect, whose identity was not immediately released, ultimately surrendered after asking officers for handcuffs, an LAPD source said.

Fire officials said six people, ranging in age from 12 to 81, were taken to hospital.

It was not clear how many people were inside the store in Silver Lake neighbourhood and whether there were any other casualties.

Atkins' grandmother initially was taken to a hospital in critical condition and police said she had been shot seven times but Egland, who visited Madison at the hospital on Sunday, said she had only been shot three times, had undergone surgery and her condition was improving. A man exited the vehicle and ran into the grocery store, said Don Kohles, 91.

"Just as I turned, I heard all these gunshots and I turned around and this vehicle crashed right in back of me", Kohles said. "I look behind me and there were two police guys coming with heavy guns, then boom, boom, boom, boom, so I go into TJ's and I see this guy and he comes in". I could tell they were employees, because they were all wearing their Hawaiian shirts, of course ... at a certain point, I did see one of the employees drag a lifeless body out, at which point 6 or 7 armed officers flanked the body and escorted it out; escorted the body out.

He then saw about five employees hang out a second-floor window and drop to the ground and about 15 other people run to safety from the back of the store. "They helped carry me across the parking lot and they sort of tossed me over a wall", Mr Kohles added.

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